A hybrid convolution quadrature-temporal Galerkin approach to the solution of multiregion, dispersive time domain electromagnetic integral equations of electromagnetics

The convolution quadrature (CQ) approach to the solution of the time domain integral equations of electromagnetics has several important advantages over the more conventional temporal Galerkin (TG) approaches. Chief among these are its highly predictable stability properties, and its applicability to dispersive media. The primary drawback of CQ-based approaches is that their model of the interaction between basis functions tends to have a lingering time history; that is, they give rise to a convolution kernel that is unnecessarily languorous. To shorten this interaction, the work presented here employs a hybrid method which combines the CQ approach with a TG approach to achieve a faster simulation with minimal dispersion in nondispersive media. In dispersive media, where the inefficiency of the CQ approach is less pronounced, CQ is left in tact. Numerical results will demonstrate that the approach is accurate and efficient for the computation of scattering from dispersive media.